# Progressive Generalization Risk Reduction for Data-Efficient Causal Effect Estimation

arXiv: https://arxiv.org/abs/2411.11256 · HTML: https://mlsanity.com/paper/2411.11256/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 56 references that are in the map.
- First posted on arXiv 18 Nov 2024.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [Self-supervised Learning: Generative or Contrastive](https://mlsanity.com/paper/2006.08218/) (2020)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [BatchBALD: Efficient and Diverse Batch Acquisition for Deep Bayesian Active Learning](https://mlsanity.com/paper/1906.08158/) (2019)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [A Survey on Causal Inference](https://mlsanity.com/paper/2002.02770/) (2020)
- [A Comparative Survey of Deep Active Learning](https://mlsanity.com/paper/2203.13450/) (2022)
- [Gone Fishing: Neural Active Learning with Fisher Embeddings](https://mlsanity.com/paper/2106.09675/) (2021)
- [On Feature Collapse and Deep Kernel Learning for Single Forward Pass Uncertainty](https://mlsanity.com/paper/2102.11409/) (2021)
- [Bayesian Batch Active Learning as Sparse Subset Approximation](https://mlsanity.com/paper/1908.02144/) (2019)
- [Identifying Causal-Effect Inference Failure with Uncertainty-Aware Models](https://mlsanity.com/paper/2007.00163/) (2020)
- [Quantifying Ignorance in Individual-Level Causal-Effect Estimates under Hidden Confounding](https://mlsanity.com/paper/2103.04850/) (2021)
- [A Framework and Benchmark for Deep Batch Active Learning for Regression](https://mlsanity.com/paper/2203.09410/) (2022)
- [Stochastic Batch Acquisition: A Simple Baseline for Deep Active Learning](https://mlsanity.com/paper/2106.12059/) (2021)
- [Benchmarking Framework for Performance-Evaluation of Causal Inference Analysis](https://mlsanity.com/paper/1802.05046/) (2018)
- [Pool-Based Sequential Active Learning for Regression](https://mlsanity.com/paper/1805.04735/) (2018)
- [Causal-BALD: Deep Bayesian Active Learning of Outcomes to Infer Treatment-Effects from Observational Data](https://mlsanity.com/paper/2111.02275/) (2021)
- [Overcoming Data Sparsity in Group Recommendation](https://mlsanity.com/paper/2010.00813/) (2020)
- [Active Learning for Decision-Making from Imbalanced Observational Data](https://mlsanity.com/paper/1904.05268/) (2019)
- [Dynamic Inter-treatment Information Sharing for Individualized Treatment Effects Estimation](https://mlsanity.com/paper/2305.15984/) (2023)
- [Sample Constrained Treatment Effect Estimation](https://mlsanity.com/paper/2210.06594/) (2022)
- [To Predict or to Reject: Causal Effect Estimation with Uncertainty on Networked Data](https://mlsanity.com/paper/2309.08165/) (2023)

## Built on by (most cited first, 3 of 3)

- [Enhancing Treatment Effect Estimation via Active Learning: A Counterfactual Covering Perspective](https://mlsanity.com/paper/2505.05242/) (2025)
- [ActiveCQ: Active Estimation of Causal Quantities](https://mlsanity.com/paper/2509.24293/) (2025)
- [Uncertainty-Guided LLM Semantic Augmentation for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2607.26599/) (2026)

## Abstract (arXiv)

Causal effect estimation (CEE) provides a crucial tool for predicting the unobserved counterfactual outcome for an entity. As CEE relaxes the requirement for ``perfect'' counterfactual samples (e.g., patients with identical attributes and only differ in treatments received) that are impractical to obtain and can instead operate on observational data, it is usually used in high-stake domains like medical treatment effect prediction. Nevertheless, in those high-stake domains, gathering a decently sized, fully labelled observational dataset remains challenging due to hurdles associated with costs, ethics, expertise and time needed, etc., of which medical treatment surveys are a typical example. Consequently, if the training dataset is small in scale, low generalization risks can hardly be achieved on any CEE algorithms. Unlike existing CEE methods that assume the constant availability of a dataset with abundant samples, in this paper, we study a more realistic CEE setting where the labelled data samples are scarce at the beginning, while more can be gradually acquired over the course of training -- assuredly under a limited budget considering their expensive nature. Then, the problem naturally comes down to actively selecting the best possible samples to be labelled, e.g., identifying the next subset of patients to conduct the treatment survey. However, acquiring quality data for reducing the CEE risk under limited labelling budgets remains under-explored until now. To fill the gap, we theoretically analyse the generalization risk from an intriguing perspective of progressively shrinking its upper bound, and develop a principled label acquisition pipeline exclusively for CEE tasks. With our analysis, we propose the Model Agnostic Causal Active Learning (MACAL) algorithm for batch-wise label acquisition, which aims to reduce both the CEE model's uncertainty and the post-acquisition ...